1996/03/21 by Nico Μ. Τemme, Temme, Nico M. · 1 citation
Mathematics · Engineering · #Mathematical functions and polynomials #Control Systems and Identification #Iterative Methods for Nonlinear Equations
paper · pdf · doi:10.48550/arxiv.math/9603218
We consider the asymptotic behavior of the incomplete gamma functions\ngamma(-a,-z) and Gamma(-a,-z) as a goes to infinity. Uniform expansions are\nneeded to describe the transition area z~a in which case error functions are\nused as main approximants. We use integral representations of the incomplete\ngamma functions and derive a uniform equation by applying techniques used for\nthe existing uniform expansions for gamma(a,z) and Gamma(a,z). The result is\ncompared with Olver's uniform expansion for the generalized exponential\nintegral. A numerical verification of the expansion is given in a final\nsection.\n